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Title: Security of quantum bit-string generation

Abstract

We consider the cryptographic task of bit-string generation. This is a generalization of coin tossing in which two mistrustful parties wish to generate a string of random bits such that an honest party can be sure that the other cannot have biased the string too much. We consider a quantum protocol for this task, originally introduced in Phys. Rev. A 69, 022322 (2004), that is feasible with present day technology. We introduce security conditions based on the average bias of the bits and the Shannon entropy of the string. For each, we prove rigorous security bounds for this protocol in both noiseless and noisy conditions under the most general attacks allowed by quantum mechanics. Roughly speaking, in the absence of noise, a cheater can only bias significantly a vanishing fraction of the bits, whereas in the presence of noise, a cheater can bias a constant fraction, with this fraction depending quantitatively on the level of noise. We also discuss classical protocols for the same task, deriving upper bounds on how well a classical protocol can perform. This enables the determination of how much noise the quantum protocol can tolerate while still outperforming classical protocols. We raise several conjectures concerning bothmore » quantum and classical possibilities for large n cryptography. An experiment corresponding to the scheme analyzed in this paper has been performed and is reported elsewhere.« less

Authors:
;  [1]
  1. Physique Theorique, C.P. 225, Universite Libre de Bruxelles, Boulevard du Triomphe, 1050 Brussels (Belgium)
Publication Date:
OSTI Identifier:
20646186
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 70; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.70.052310; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; CORRELATIONS; ENERGY LEVELS; ENTROPY; INFORMATION THEORY; NOISE; QUANTUM MECHANICS; RANDOMNESS; SECRECY PROTECTION

Citation Formats

Barrett, Jonathan, Massar, Serge, and Centre for Quantum Information and Communication, C.P. 165/59, Universite Libre de Bruxelles, Avenue F.D. Roosevelt 50, 1050 Brussels. Security of quantum bit-string generation. United States: N. p., 2004. Web. doi:10.1103/PhysRevA.70.052310.
Barrett, Jonathan, Massar, Serge, & Centre for Quantum Information and Communication, C.P. 165/59, Universite Libre de Bruxelles, Avenue F.D. Roosevelt 50, 1050 Brussels. Security of quantum bit-string generation. United States. https://doi.org/10.1103/PhysRevA.70.052310
Barrett, Jonathan, Massar, Serge, and Centre for Quantum Information and Communication, C.P. 165/59, Universite Libre de Bruxelles, Avenue F.D. Roosevelt 50, 1050 Brussels. 2004. "Security of quantum bit-string generation". United States. https://doi.org/10.1103/PhysRevA.70.052310.
@article{osti_20646186,
title = {Security of quantum bit-string generation},
author = {Barrett, Jonathan and Massar, Serge and Centre for Quantum Information and Communication, C.P. 165/59, Universite Libre de Bruxelles, Avenue F.D. Roosevelt 50, 1050 Brussels},
abstractNote = {We consider the cryptographic task of bit-string generation. This is a generalization of coin tossing in which two mistrustful parties wish to generate a string of random bits such that an honest party can be sure that the other cannot have biased the string too much. We consider a quantum protocol for this task, originally introduced in Phys. Rev. A 69, 022322 (2004), that is feasible with present day technology. We introduce security conditions based on the average bias of the bits and the Shannon entropy of the string. For each, we prove rigorous security bounds for this protocol in both noiseless and noisy conditions under the most general attacks allowed by quantum mechanics. Roughly speaking, in the absence of noise, a cheater can only bias significantly a vanishing fraction of the bits, whereas in the presence of noise, a cheater can bias a constant fraction, with this fraction depending quantitatively on the level of noise. We also discuss classical protocols for the same task, deriving upper bounds on how well a classical protocol can perform. This enables the determination of how much noise the quantum protocol can tolerate while still outperforming classical protocols. We raise several conjectures concerning both quantum and classical possibilities for large n cryptography. An experiment corresponding to the scheme analyzed in this paper has been performed and is reported elsewhere.},
doi = {10.1103/PhysRevA.70.052310},
url = {https://www.osti.gov/biblio/20646186}, journal = {Physical Review. A},
issn = {1050-2947},
number = 5,
volume = 70,
place = {United States},
year = {2004},
month = {11}
}